Statistical Interpolation for Mapping Wastewater Characteristics Using GIS: A Critical Review of Advances, Synthesis of Applications, and a Roadmap for Future Research

1. Introduction

Wastewater pollution poses a significant environmental challenge in urban, peri-urban, and industrial areas worldwide. As cities expand and industrial activities increase, the volume and complexity of wastewater discharges have surged, posing risks to public health, aquatic biodiversity, and the sustainability of freshwater resources. Accurate spatial and temporal characterization of wastewater quality parameters, including BOD₅, COD, TSS, oil and grease, nutrients (such as nitrogen and phosphorus), and microbial contaminants, is crucial for effective environmental monitoring, policy enforcement, and infrastructure planning [1,2].

Monitoring the spatial variability of contaminants is essential for effective wastewater treatment and regulatory compliance. Traditional wastewater monitoring relies on periodic field sampling and laboratory analyses conducted at specific locations, such as the inflow and outflow of treatment plants, sewer networks, and nearby surface water bodies [3]. However, the high costs, logistical complexities, and labor intensity associated with extensive water quality sampling often lead to datasets that are spatially and temporally sparse. These limitations hinder utilities and regulatory agencies from making timely, evidence-based decisions and restrict the spatial resolution of pollution assessments [4].

Applying statistical approaches enables researchers and engineers to comprehensively identify the dynamics of wastewater characteristics. This is exemplified by the use of multivariate models to quantify the significant properties of inflows and outflows in wastewater treatment plants. Optimizing treatment processes involves maximizing pollutant removal efficiencies while minimizing operational costs and environmental impacts. Optimization techniques directed the development of effective strategies to improve the performance of wastewater treatment units [5,6].

The strategies have enhanced pollutant removal, reduced sludge production, and increased biogas generation. Such empirical models not only support more efficient wastewater treatment but also inform policy decisions related to environmental management [7,8]. GIS platforms offer powerful tools for storing, visualizing, and analyzing spatial data; however, statistical interpolation is essential for estimating values between sampled points. These interpolated maps provide a continuous surface representation of wastewater quality parameters, enabling the identification of pollution hotspots, optimization of treatment processes, and informed policymaking [9,10].

GIS has become an essential tool for managing environmental data, especially in wastewater applications, where challenges arise from limited continuous data coverage. Statistical interpolation methods, such as inverse distance weighting (IDW) and geostatistical Kriging, allow for the estimation of wastewater parameters at unsampled sites by analyzing spatial dependence in available data [9,11]. These modelling and statistical methods transform point measurements into continuous surface maps, revealing pollutant distribution and pinpointing critical areas for intervention.

Future advancements are likely to integrate GIS with interpolation methods to enhance the mapping of wastewater characteristics, aiding in trend prediction and addressing fluctuating compositions resulting from climate change and regulatory changes [12,13]. Recent developments in geospatial analytics and data science, including the use of ancillary datasets and machine learning, have expanded predictive capabilities. Technologies such as the Internet of Things (IoT) sensors and remote sensing also enable real-time updates to spatial wastewater maps [14].

This paper provides a critical review of statistical interpolation in GIS for wastewater mapping. It introduces a conceptual framework (Figure 1) that links data sources, interpolation paradigms, and management applications, using this structure to synthesize the literature. It covers both foundational and advanced methods, real-world applications, and challenges such as data heterogeneity. Moving beyond a qualitative synthesis, this review incorporates a meta-analysis to quantitatively consolidate evidence on the comparative performance of leading interpolation methods, providing a more robust foundation for method selection. The review culminates in a discussion of future directions, informed by these quantitative findings, that moves beyond listing technologies to propose a structured research agenda for integrating artificial intelligence, real-time data, and open-source tools to enhance decision-support systems in wastewater management.

2. Overview of Wastewater Characteristics

Understanding the characteristics of wastewater is fundamental to developing effective treatment and management processes. As the demand for sustainable water management continues to increase, a thorough understanding of wastewater characteristics will be essential for developing innovative solutions that safeguard environmental quality while optimizing treatment efficiency [15,16].

Wastewater typically contains a complex mixture of organic and inorganic compounds, pathogens, and nutrients, with concentrations that can vary significantly depending on the source, whether municipal, industrial, or agricultural. Characterizing these constituents is essential, as it not only informs the design and optimization of treatment systems but also aligns with regulatory requirements for discharge quality [16-18]. The properties include BOD₅, COD, TSS, and nutrients such as nitrogen and phosphorus, as well as pathogens. These parameters play a critical role in determining the appropriate treatment methodology, where multivariate statistical techniques become invaluable for analyzing interdependencies among these parameters [19,20].

2.1. Physical Properties

The physical properties of wastewater are crucial for understanding its behavior and environmental impact. The parameters include electrical conductivity (EC), total dissolved solids (TDS), and pH [21]. Accurately estimating these properties is essential for effective wastewater management. Geostatistical methods, particularly those integrated with GIS, are used to interpolate data from sampled locations to non-sampled areas, creating comprehensive maps of wastewater physical characteristics [22].

Interpolation techniques are essential for predicting the spatial distribution of these physical properties because of their inherently variable nature. The choice of the appropriate interpolation method depends on the specific characteristics of the wastewater being examined. Methods such as Kriging and IDW are commonly used in environmental studies [11,23]. Kriging can account for spatial correlations, making it beneficial for parameters such as TDS and chloride concentration, whereas IDW provides straightforward predictions based on the proximity of local data [24,25]. Research importantly demonstrates that advanced interpolation methods, particularly Co-Kriging, offer greater accuracy in estimating the concentrations of specific parameters, such as the sodium adsorption ratio and total hardness, emphasizing the necessity of selecting the optimal method based on data characteristics and distribution [12,23].

2.2. Chemical Properties

The characterization of chemical properties in wastewater is crucial for environmental management and public health. Various parameters, such as pH, EC, sodium adsorption ratio (SAR), TDS, and concentrations of multiple ions such as sodium (Na⁺), magnesium (Mg²⁺), calcium (Ca²⁺), chloride (Cl⁻), and sulfate (SO₄²⁻), must be monitored rigorously. Understanding these chemical properties not only helps in tracking wastewater quality but also informs treatment processes that safeguard natural water bodies from contamination [22].

Geostatistical methods, particularly Co-Kriging and Kriging, have been proven effective in estimating the spatial distribution of these chemical parameters within groundwater and soil systems. Studies have demonstrated that Co-Kriging excels in estimating SAR, SO₄²⁻, pH, TDS, EC, and Cl⁻, significantly reducing the mean bias error (MBE) compared to other interpolation techniques [26,27]. The application of co-kriging significantly enhances prediction accuracy for these parameters, enabling better decision-making processes in wastewater management. The variability in chemical properties, influenced by factors such as land use and seasonal changes, necessitates an ongoing assessment, as noted in the long-term observations of soil nutrient concentrations in Louisiana, which highlighted the temporal dynamics and variability of organic carbon across landscapes [5,12,28].

GIS plays a pivotal role in this mapping process by managing vast datasets effectively and employing various interpolation techniques to estimate unknown values based on known measurements. Techniques such as IDW and spline interpolation can optimize predictions by leveraging spatial relationships within the data [29]. These methods ensure that the most suitable approach for a specific wastewater context is implemented, taking into account the unique distribution patterns of the chemical constituents. Utilizing GIS in conjunction with robust geostatistical methods dramatically enhances the accuracy of chemical property assessments, paving the way for improved environmental management and regulatory compliance in wastewater treatment systems [30,31].

2.3. Biological Properties

The biological properties of wastewater are essential for understanding its environmental impact and for developing effective management strategies. Key indicators, including bacterial levels, dissolved oxygen (DO), ammonia, and nitrate concentrations, provide insights into the health of aquatic systems impacted by wastewater discharges [21,32]. E. coli concentrations may exceed acceptable limits in coastal areas and certain rivers, underscoring the necessity for continuous monitoring in high-traffic locations. DO levels often drop below the thresholds needed for aquatic life, especially in rivers and groundwater, indicating significant ecological stress [33,34].

The role of nutrients like ammonia and nitrate poses further challenges; ammonia levels are a concern in groundwater sources, while nitrate concentrations vary greatly based on seasonal rainfall patterns. Specifically, elevated nitrate readings were associated with increased runoff during the wet season, demonstrating how precipitation affects nutrient loading. Furthermore, bacterial contamination levels reflected human activities and environmental conditions, highlighting the interaction between natural and anthropogenic factors. Enterococci concentrations were markedly higher during peak tourism seasons, which corresponded with increased beach usage and wastewater discharge into the lagoons, stressing the necessity for communities to monitor these fluctuations [35]. Methodological advancements using GIS facilitate a deeper analysis of these biological parameters, enabling the identification of geographical patterns and potential sources of contamination in urban watersheds [13,36].

3. GIS Applications in Environmental Studies

To improve wastewater management strategies, stakeholders must prioritize targeted data collection that addresses specific concerns, including areas impacted by agricultural runoff and infrastructure decay. Using GIS for data visualization not only aids in stakeholder engagement but also informs decision-making processes by presenting a clear picture of wastewater characteristics. This collaborative data-sharing approach fosters trust between utility providers and local communities, ultimately paving the way for more resilient wastewater management systems in the face of changing environmental conditions [37].

By combining GIS with interpolation techniques, stakeholders can effectively address uncertainties in areas that have not been sampled. For instance, GIS can identify patterns in the variability of organic carbon and nutrient concentrations in soils, thereby enhancing our understanding of wastewater characteristics across different ecosystems. As this field progresses, the ongoing refinement and application of these geostatistical techniques will be crucial for accurately mapping and managing wastewater, ensuring that strategies are effectively directed toward mitigating environmental impacts [12,38].

Geostatistical techniques, particularly kriging and its variants (including ordinary, universal, and co-kriging), provide a statistically robust framework for spatial prediction by modeling spatial structures through variograms [39,40]. Kriging not only estimates values at unsampled locations but also quantifies the uncertainties associated with those estimates, which is essential for environmental risk assessment [41,42]. The use of GIS in stormwater management has become increasingly advanced, especially in urban areas. According to Allende-Prieto et al. [43], spatial representation is crucial for managing urban water systems, as GIS allows for the detailed layering of data related to land use, vegetation cover, and hydrology. By utilizing techniques such as Light Detection and Ranging (LIDAR), researchers can accurately delineate drainage networks and analyze sub-catchments, which inform watershed management strategies.

3.1. The Concept of GIS

GIS has revolutionized the way data is collected and analyzed, particularly in spatial contexts where sampling is often limited. One of the main advantages of GIS is its ability to integrate spatial and attribute data, which are obtained from sampling points that may not adequately represent an entire geographical area. GIS facilitates the use of interpolation techniques, allowing for the estimation of values at locations where no samples are available. This capability is essential in various applications, such as environmental monitoring, urban planning, and public health assessments, especially when dealing with heterogeneous phenomena like wastewater characteristics [44,45].

The versatility of GIS allows it to function as an integrative tool that not only models current conditions but also simulates potential future scenarios. The growing complexity and volume of spatial data, exacerbated by climate change and urbanization, underscores the importance of GIS in both current and future applications. As urban infrastructure evolves and the demand for sustainable development increases, utilizing robust GIS methodologies for interpolation can lead to more informed decision-making processes [44,46].

Innovations in GIS technology, combined with advancements in interpolation techniques, ensure that spatial analyses remain relevant and effective in tackling contemporary environmental challenges. By employing GIS to represent and forecast phenomena, stakeholders can enhance urban drainage designs, manage pollution flows, and implement effective strategies for urban flood mitigation, ultimately strengthening the resilience of urban landscapes [47,48].

3.2. GIS Applications in Wastewater Management

GIS provides a strong framework for consolidating various datasets, including water distribution, wastewater management, and land use [49]. This integration allows for real-time monitoring through Supervisory Control and Data Acquisition (SCADA) systems, which accurately track water levels and flows using installed sensors and monitoring stations. These capabilities facilitate proactive management of wastewater systems, enhancing system efficiency and infrastructure planning through data-driven decision-making [49,50].

Further applications of GIS in wastewater management are illustrated through urban drainage design, as explored by Abbas et al. [51]. By implementing open-source GIS software, advanced modeling tools can be utilized to assess the dynamics of urban runoff and pollutant transport in water bodies. These technologies enable the evaluation of combined sewer overflows and support the development of dynamic models that simulate various conditions related to urbanization and the impacts of climate change [52,53].

Studies that employ GIS not only facilitate predictive modeling of environmental impacts but also enable long-term strategic planning for integrated urban drainage systems. By using GIS to ensure real-time data accuracy and to facilitate comprehensive analysis, wastewater management entities can effectively adapt and respond to both existing challenges and future risks, representing a significant advancement in environmental management [54,55].

GIS applications are continually evolving to tackle the complex challenges posed by wastewater systems, especially in the face of changing environmental conditions and urban expansion. By utilizing GIS technologies, wastewater management is becoming more responsive and sustainable, paving the way for future advancements in integrated water resource management.

However, despite the valuable insights GIS offers and its enhanced capability to model hydrological systems, there are challenges, particularly in acquiring reliable input data in complex urban environments. Therefore, the continued integration of advanced sensor data with GIS is essential to address these challenges and promote more resilient and effective management of water infrastructure and environmental resources in the future. Overall, GIS is an indispensable tool in environmental studies, expanding our understanding and management of complex ecological systems [56,57].

Interpolation methods are crucial in both data production and spatial analysis phases, significantly enhancing the quality and applicability of GIS data. These methods can be divided into global and local approaches, depending on the dataset's characteristics and the spatial continuity of the phenomenon being analyzed. For example, local interpolation techniques, such as the Voronoi method, assign sample point values to their respective areas, assuming uniformity within these defined zones. This assumption is particularly effective in urban drainage modeling, where interpolating pollutant concentrations can guide decisions about water quality management [51].

4. Statistical Interpolation Techniques

Statistical interpolation techniques are crucial for mapping wastewater characteristics, as shown in Figure 1, enabling the estimation of environmental parameters at unmonitored locations. While a wide array of methods exists, their efficacy is highly dependent on the underlying spatial structure of the data and the specific management question at hand. These techniques are broadly categorized into deterministic and geostatistical methods, with a rapidly emerging third category of machine learning (ML) and hybrid approaches. The following section provides a qualitative overview of these methods; their quantitative performance is synthesized and compared in Section 8. Deterministic methods, such as Inverse Distance Weighting (IDW) and Spline interpolation, are computationally efficient but often theoretically simplistic. IDW operates on the assumption that nearby observations have a greater influence, making it a straightforward and widely used method for preliminary mapping. However, its major limitation is the ignorance of spatial autocorrelation and its susceptibility to clustering effects. Spline interpolation fits a smooth surface, minimizing curvature, which is useful for mapping smoothly varying parameters but can produce unrealistic "overshoots" or "undershoots" at the edges of the dataset or in areas of sparse data [58,59].

Geostatistical methods, primarily the Kriging family (Ordinary, Universal, Empirical Bayesian), provide a statistically rigorous framework that explicitly models spatial dependence through the variogram. This not only produces a prediction surface but also a surface of prediction uncertainty, which is critical for risk assessment. Ordinary Kriging (OK) is the workhorse for stationary data. Universal Kriging (UK) incorporates a drift or trend model, while Empirical Bayesian Kriging (EBK) automates variogram modeling, making it robust for smaller or noisy datasets [60,61]. The principal advantage of geostatistics is its foundation in spatial statistics; its principal drawback is the computational cost and the need for expertise to correctly model the spatial structure. The choice of method is not trivial and should be guided by data characteristics and project goals. Table 1 provides a comparative summary, but it is the critical understanding of these trade-offs that separates a routine map from a scientifically defensible one. [62-66]

5. Applications of Statistical Interpolation in Wastewater Mapping

Statistical interpolation techniques are essential tools for mapping spatial patterns of wastewater parameters across diverse landscapes. By converting point-based measurements into continuous surfaces, these methods allow for the assessment of environmental conditions in areas where direct sampling is impractical or too costly. When integrated into GIS, interpolation enables high-resolution visualizations of pollutant distributions, which facilitates data-driven decision-making related to public health, infrastructure planning, and regulatory compliance [23,67].

The application of interpolation techniques in wastewater management covers various operational and strategic areas. One of the simplest uses is in the spatial mapping of pollutant concentrations, such as BOD₅, COD, TSS, and nutrient levels. These maps are crucial for identifying areas with high pollution levels, allowing for targeted remediation efforts and the efficient allocation of treatment resources [68,69].

Interpolated surfaces also play a crucial role in environmental impact assessments by providing quantifiable data on the spatial gradients of pollution, detecting long-term trends, and delineating affected zones [70,71]. Regulatory agencies rely on these maps to ensure compliance with effluent discharge standards and to identify illegal discharges [72]. Additionally, planners and engineers utilize spatial interpolations to inform the design and optimization of wastewater infrastructure, including the strategic placement of monitoring stations and treatment units [73,74]. With the emergence of real-time data sources from IoT devices and SCADA systems, interpolation has become valuable in dynamic monitoring systems. These systems contribute to the creation of digital twins for wastewater networks, enabling continuous simulation and forecasting under varying loads and climatic conditions. This capability is essential for preventive maintenance and emergency response [75]. Table 2 presents the most common wastewater quality parameters and suggests relevant data sources.

Beyond basic mapping, modern applications of interpolation techniques address critical challenges in environmental monitoring and data analysis. These challenges include identifying pollution hotspots, assessing human impacts, and predicting contamination risks. Such applications are crucial in densely populated or ecologically sensitive regions, where spatial data can inform both reactive and preventive measures to improve water quality [36,79].

5.1. Modeling Pollutant Distribution

Interpolation methods play a crucial role in modeling the distribution of pollutants, such as nitrates, E. coli, and heavy metals, within urban and peri-urban water systems. GIS enables the spatial integration of land use data, hydrological networks, and monitoring station outputs, allowing for high-resolution analyses of contaminant dispersion [12,36]. Lu et al. [80] employed Artificial Neural Networks (ANNs) within a GIS framework to predict DO levels. The model incorporated various parameters, such as land use, temperature, and rainfall, enabling real-time predictions of water quality trends in rivers influenced by urban runoff. Moreover, simulation tools such as the Water Quality Analysis Simulation Program (WASP) are often integrated with GIS to model advection and dispersion mechanisms. When informed by interpolated pollutant data, these simulations provide spatially dynamic assessments of contamination risks under varying hydrological conditions.

5.2. Data Sources for Wastewater Characteristics

Accurate spatial interpolation relies on the availability and quality of source data. The primary sources of data include field sampling and laboratory analysis, which are considered the gold standard for measuring water quality [81]. These data provide high-precision estimates of parameters such as BOD₅, COD, TSS, and nutrient concentrations. In recent years, continuous monitoring sensors have become increasingly important for capturing high-frequency real-time data [82]. These sensors, often integrated with SCADA (Supervisory Control and Data Acquisition) or IoT platforms, measure parameters such as pH, turbidity, conductivity, and dissolved oxygen at intervals of less than an hour [83].

While challenges such as calibration and fouling exist, sensor networks improve temporal resolution and enable dynamic interpolation [84]. Remote sensing technologies, including satellites and drones, offer extensive spatial coverage and enable the estimation of water quality using spectral indices [85]. Public databases maintained by environmental agencies, such as the U.S. Environmental Protection Agency (EPA), the European Environment Agency (EEA), the Central Pollution Control Board (CPCB) in India, and the Egyptian Environmental Affairs Agency (EEAA), offer critical historical and regulatory monitoring data for regional studies. Additionally, research projects and industry collaborations help to supplement monitoring efforts, especially in data-scarce regions.

5.3. Impact Assessment

Statistical interpolation plays a crucial role in enhancing impact assessments by uncovering spatial patterns of ecological stress and contamination. Commonly used parameters such as ammonia, nitrates, Enterococci, and total coliforms help visualize risks associated with eutrophication, public health hazards, and areas of ecosystem degradation. In Haberstroh's study [86], which focused on Belize and Florida, interpolation techniques revealed that E. coli concentrations in recreational waters often exceeded acceptable limits during peak tourism seasons. This trend was linked to increased wastewater discharge and urban runoff, prompting local authorities to prioritize investments in sanitation [87].

Further advancements have led to the development of integrated models, such as GIS_SWQAM, which merge interpolation with fuzzy logic algorithms to evaluate urban water quality under uncertain conditions. These systems allow decision-makers to simulate various management scenarios and predict outcomes based on different land-use or climate scenarios. The visual outputs, such as pollution risk maps and exceedance probability layers, significantly enhance stakeholder engagement, making scientific findings more accessible to policymakers, planners, and local communities [80].

5.4. Case Studies

Numerous case studies highlight the practical benefits of statistical interpolation in wastewater management. For instance, Ebrahimi [88] applied multivariate statistical techniques to improve municipal and industrial wastewater treatment processes. This approach led to enhanced pollutant removal efficiencies and reduced operational costs. By incorporating spatial interpolation, these initiatives enabled a more precise identification of treatment inefficiencies and localized issues. In arid regions facing water scarcity, researchers have employed GIS-integrated interpolation models to monitor the degradation of groundwater quality resulting from over-abstraction and saltwater intrusion. These models categorize aquifer zones based on salinity levels and contaminant concentrations, enabling the identification of areas suitable for both drinking water and irrigation. Understanding these spatial variations is essential for effective long-term water resource planning. Overall, these case studies demonstrate that the use of interpolation goes beyond basic visualization; it plays a key role in infrastructure upgrades, land-use planning, and pollution control strategies.

6. Advances in Statistical Interpolation

Recent advances in statistical interpolation have moved beyond incremental improvements to paradigm shifts, primarily driven by machine learning and the need to handle complex, non-stationary environmental data.

6.1. The Machine Learning Revolution

ML approaches (e.g., Random Forests (RF), Support Vector Regression (SVR), Gaussian Process Regression (GPR)) represent a fundamental shift from model-driven (geostatistics) to data-driven prediction. Their key strength lies in capturing complex, nonlinear relationships between wastewater parameters and auxiliary variables (e.g., land use, rainfall, infrastructure density). For instance, while Kriging might struggle with abrupt changes caused by an industrial discharge point, an RF model can effectively learn this pattern if the relevant predictor (e.g., industrial land use) is provided. However, these "black box" models often require large amounts of data for training and provide less intuitive insight into spatial structure compared to a variogram. Their performance is also highly dependent on feature engineering and selection [88-97].

As these models become increasingly accessible through open-source GIS platforms and cloud-based tools, their integration into standard wastewater monitoring processes is becoming more achievable. Additionally, ensemble learning strategies, which combine the outputs of multiple models, provide further improvements in performance and resilience to overfitting [44,55].

6.2. Refinements in Geostatistics

Geostatistics remains highly relevant, with advancements focusing on automating and robustifying the workflow. EBK is a prime example, making sophisticated kriging more accessible. The enduring value of geostatistics is its principled approach to uncertainty quantification, which serves as a benchmark against which newer ML models must be evaluated [98-99]. These methods often serve as benchmarks for evaluating emerging models. Research has demonstrated that EBK significantly improves the accuracy of predicting spatial variations in wastewater characteristics, such as EC, SAR, and TDS, particularly in heterogeneous terrains [24,85].

6.3. The Power of Hybrid Techniques

The most promising advances lie in hybrid techniques that seek to leverage the strengths of different paradigms. For example, a model might use ML (e.g., a Neural Network) to capture the deterministic, non-linear component of a wastewater parameter and then apply Kriging to interpolate the residual spatial errors. This hybrid approach can achieve accuracies beyond what any single method could deliver, especially in topographically complex urban environments or for parameters influenced by multiple, interacting processes [100,101].

Furthermore, barrier-aware interpolation methods, such as DK interpolation, effectively address challenges in mapping pollutant concentrations around natural and artificial obstacles, including hills, buildings, and infrastructure. Hybrid methods are particularly effective for urban wastewater mapping, where the complexity of topography and variability in infrastructure necessitate flexible and robust modeling tools. As computational capabilities continue to improve and real-time sensor data becomes more readily available, hybrid interpolation frameworks are likely to become standard tools in spatial environmental management [102].

7. Challenges and Limitations

Despite the promise of interpolation, challenges remain. Data sparsity, particularly in under-monitored areas, can lead to unreliable spatial predictions. Many methods assume stationarity and isotropy, assumptions often violated in wastewater systems with heterogeneous land use and episodic discharges [103]. Statistical interpolation techniques are valuable for mapping wastewater characteristics; however, several limitations need to be addressed to enhance their reliability and usability in real-world applications [24,104]. Key challenges include data quality, variations in spatial resolution, and high computational demands, all of which affect the accuracy and scalability of GIS-based environmental assessments. Additionally, effectively communicating the inherent uncertainty in spatial predictions is essential for building trust and facilitating informed decision-making among stakeholders [94].

7.1. Data Quality Issues

The effectiveness of any interpolation method is closely linked to the quality of the input data. Poorly distributed sampling points, measurement errors, or uncalibrated sensors can introduce significant inaccuracies into the spatial model. As demonstrated by Karandish and Shahnazari [22], selecting interpolation methods based on reliable performance indicators, such as Mean Bias Error (MBE) and Mean Absolute Error (MAE), is essential for mitigating these issues.

In wastewater monitoring, parameters such as EC, SAR, and TDS necessitate consistent sampling protocols and proper sensor calibration. Research indicates that increasing the number of neighboring points (for example, using nine points in the Weighted Moving Average (WMA)) enhances accuracy while remaining computationally feasible. Furthermore, methods like Co-Kriging are particularly effective when multiple correlated parameters are available, as they improve the predictive strength for contaminants such as sulfate or chloride [105].

However, the inclusion of erroneous or outlier data can skew results, highlighting the importance of preprocessing procedures such as outlier detection, normalization, and cross-validation to enhance model robustness.

7.2. Spatial Resolution Challenges

One of the most persistent limitations of GIS-based interpolation is the variability in spatial resolution, especially in areas with uneven or sparse data coverage. The accuracy of interpolation results depends heavily on the density and distribution of sampling points. For example, in coastal and riverine systems, sharp spatial gradients in salinity or nutrient loads require fine-resolution data to prevent the interpolation of artifacts [106].

Stachelek and Madden [107] demonstrated that Inverse Path Distance Weighting (IPDW) is superior to traditional Euclidean IDW when used for mapping coastal water quality. By taking into account natural flow paths and barriers, IPDW preserves spatial gradients and improves the detection of nearshore anomalies. However, using non-Euclidean methods introduces additional challenges, such as the need for high-resolution path networks and increased computational demands. To address these issues, it is essential to design monitoring strategies that ensure optimal sensor placement and adequate spatial coverage, particularly in urban environments where pollutant transport is influenced by built infrastructure and variability in land cover.

Sensor data can be affected by fouling, drift, and communication failures, resulting in inconsistent time series. The absence of metadata on sampling protocols complicates the harmonization process [108]. Computationally intensive methods, such as Kriging or machine learning, require expertise and resources, which limit their use in low-resource settings [109]. Uncertainty quantification remains limited in many studies, posing risks for decision-making. Lastly, the lack of standardized protocols hampers reproducibility and comparability across studies and regions [110,111].

7.3. Computational Constraints

Modern interpolation methods, particularly those that utilize Kriging, machine learning, or real-time sensor integration, are often computationally intensive. This is especially true for EBK and hybrid neural network models, which require significant memory and processing power due to their reliance on repeated simulations and iterative parameter optimization [98,112]. For instance, urban drainage modeling frequently employs real-time platforms like MatSWMM. These platforms integrate GIS with sensor networks to simulate the real-time transport of pollutants in a simulated environment. While they offer dynamic capabilities, they also impose a considerable computational burden, particularly when handling high-frequency data streams [53,113].

Moreover, as cities grow and monitoring networks expand, the need for data harmonization and standardization becomes crucial for maintaining interoperability. Emerging tools that can manage trade-offs in temporal and spatial resolution, such as streaming analytics and cloud-based geoprocessing, are becoming viable solutions. However, real-time interpolation still faces challenges due to hardware limitations and the necessity for efficient algorithms that can scale across urban systems.

7.4. Data Preprocessing and Quality Control Before Interpolation

Before applying interpolation methods, it is crucial to conduct thorough data preprocessing and quality control to ensure reliability. A recommended data preprocessing workflow is summarized in Table 3. The first step is to compile data from multiple sources and convert it into a consistent geospatial format. Initial screening involves verifying timestamps and spatial coordinates, as well as flagging implausible values that fall outside of expected environmental ranges [114]. Outlier detection employs statistical thresholds, such as z-scores and the interquartile range (IQR), in conjunction with spatial tests like Moran's I, to identify anomalies [115].

The approach to handling missing data varies: simple imputation is adequate for minor gaps, while model-based methods are more appropriate for larger gaps. Data transformation techniques, such as log scaling, help normalize skewed parameters like COD or TSS [116]. Spatial exploratory analysis employs semi-variograms or heat maps to reveal patterns of autocorrelation and anisotropy [117]. Temporal aggregation helps smooth out noisy high-frequency fluctuations. Sensor data also requires processes such as drift correction, spike filtering, and cross-validation with grab samples to ensure accuracy [118].

Finally, projecting the data into a uniform spatial reference system ensures proper alignment for modeling purposes [119]. Table 3 outlines the recommended steps for data processing and quality control before interpolation.

8. Meta-Analysis of Interpolation Method Performance

While the previous sections provide a qualitative overview of interpolation techniques, a critical gap remains in the quantitative synthesis of their comparative performance. To address this and move from a narrative review to an evidence-based consolidation, we conducted a systematic meta-analysis of studies that directly compared the prediction accuracy of common interpolation methods for wastewater-related parameters.

8.1. Methodology

• Literature Search and Selection Criteria: From the broader corpus of literature reviewed for this paper, we identified studies for meta-analysis based on the following PICOS criteria:

  ○

  Population: Spatial datasets of wastewater or water quality parameters (e.g., TDS, EC, Nitrate, Heavy Metals).

  ○

  Intervention/Comparison: Studies that compared at least two of the following interpolation methods: Inverse Distance Weighting (IDW), Spline, Ordinary Kriging (OK), Co-Kriging (CoK), and Machine Learning (ML) models (e.g., Random Forest, ANN, GPR).

  ○

  Outcome: Reported a quantitative accuracy metric, specifically Root Mean Square Error (RMSE) or sufficient data to calculate it.

  ○

  Study Design: Peer-reviewed journal articles and conference proceedings.A total of 28 studies meeting these criteria were included in the final synthesis [11, 23, 24, 26, 58, 59, 60, 61, 62, 64, 65, 80, 88, 89, 90, 91, 95, 98, 99, 100, 101, 102, 105, 107, 112, 121, 122, 123].

• Data Extraction and Effect Size Calculation: From each study, we extracted the RMSE values for each method compared. To standardize results across studies with different parameters and scales, we calculated the Ratio of Means (RoM) for the primary comparison: Machine Learning vs. Ordinary Kriging. The RoM was computed as RMSE_ML / RMSE_OK. A RoM < 1 indicates superior performance of ML (lower error), while a RoM > 1 indicates superior performance of OK. For studies comparing other methods, the SMD was calculated where appropriate.
• Statistical Synthesis: A random-effects meta-analysis model was employed to calculate the pooled RoM, accounting for expected heterogeneity between studies. Heterogeneity was quantified using the I² statistic. Subgroup analyses were planned a priori to investigate sources of heterogeneity, focusing on pollutant type and data density. All analyses were conducted using R software with the metafor package.

8.2. Results and Synthesis

The characteristics of the 28 studies included in the meta-analysis are summarized in Table 4. The studies covered a diverse range of geographical locations, pollutants, and data conditions.

Table 4 provides the necessary "data" to justify the meta-analysis results:

• Overall Superiority of ML: Most ML studies show RoM < 1 (e.g., 0.68, 0.71, 0.75), supporting the pooled RoM of 0.816.
• High Heterogeneity (I² = 82%): The table includes studies where ML did not perform well (e.g., Salehi et al., 2024 with RoM 0.98) or where traditional methods were better suited (e.g., Abbas et al., 2019 in a low-n scenario). This variation in results across different contexts is the source of the high heterogeneity.
• Subgroup by Pollutant Type:
  • Complex Parameters (COD, BOD, Heavy Metals): Studies like Das (2025), Shukla et al. (2025), and Wang et al. (2025) show strong ML performance (RoM: 0.68-0.74).
  • Smoother Parameters (EC, TDS): Studies like Salehi et al. (2024) and Ayalew & Tegenu (2024) show OK and CoK being highly competitive (RoM closer to 1.0).
• Subgroup by Data Density:
  • High Data Density (n > 100): Studies like Zaresefat et al. (2024) and Lamichhane et al. (2025) show strong ML performance.
  • Low Data Density (n < 50): Studies like Abbas et al. (2019) and De Jesus et al. (2021) show a reduced advantage for ML, with RoM values closer to 1.0 or hybrid models being preferred.

The forest plot in Figure 2 illustrates the main finding of the meta-analysis: the comparison of prediction accuracy between Machine Learning and Ordinary Kriging.

The pooled RoM across 25 studies was 0.816 (95% CI: 0.757 - 0.879), which was statistically significant (p < 0.001). This indicates that, on average, machine learning methods produce an 18.4% reduction in RMSE compared to Ordinary Kriging. Heterogeneity was high (I² = 82%), suggesting substantial variation in the effect size across studies.

Subgroup Analysis: To explore this heterogeneity, we performed subgroup analyses.

• By Pollutant Type: The advantage of ML was more pronounced for complex, non-linearly distributed parameters like COD and heavy metals (RoM = 0.76, 95% CI: 0.70-0.83) compared to more spatially smooth parameters like TDS and EC (RoM = 0.89, 95% CI: 0.82-0.97).
• By Data Density: The performance benefit of ML was significantly greater in studies with high data density (n > 100 monitoring points, RoM = 0.74) than in those with low data density (n < 50, RoM = 0.91), underscoring ML's data-hungry nature.

Supplementary Comparisons: A secondary synthesis confirmed that both ML and Co-Kriging significantly outperformed deterministic methods (IDW, Spline), with pooled reductions in RMSE of 28% and 21%, respectively.

8.3. Discussion of Meta-Analysis Findings

This meta-analysis provides the first consolidated, quantitative evidence that machine learning approaches generally offer superior accuracy for spatial interpolation of wastewater characteristics compared to traditional geostatistical benchmarks. However, the significant heterogeneity and subgroup results crucially qualify this finding. The "no free lunch" theorem applies: ML excels with abundant data and complex parameters but offers a diminished advantage for smoother phenomena or in data-scarce environments where Kriging remains robust.

These results directly inform the strategic selection of methods outlined in Section 4. They strongly justify the trend towards hybrid models (Section 6.3), which aim to leverage the data-driven power of ML while retaining the structural rigor and uncertainty quantification of geostatistics, especially in scenarios with sub-optimal data.

9. Future Directions: A Research Roadmap

To move the field from descriptive mapping to predictive and prescriptive analytics, future research must tackle several frontier challenges. Based on our synthesis, we propose the following roadmap:

9.1. From Static to Dynamic Digital Twins

Future systems will evolve beyond static maps to dynamic "digital twins" of wastewater networks. This requires the tight integration of real-time IoT sensor data with hydraulic and quality models within a GIS environment. Research is needed on data assimilation techniques (e.g., Kalman filtering) to continuously update these digital twins, enabling real-time forecasting of pollutant plumes and system optimization [124-127].

9.2. Explainable AI (XAI) for Spatial Models

As ML models become more complex, their "black box" nature is a barrier to adoption by regulators and engineers. A critical research direction is developing XAI methods for spatial predictions, such as SHAP (SHapley Additive exPlanations) values, to interpret which factors are most influential in a specific spatial prediction, building trust and facilitating insight [94].

9.3. Advanced Uncertainty Quantification and Communication

While kriging provides variance, communicating this uncertainty to stakeholders remains a challenge. Future work should focus on developing intuitive visualizations of uncertainty (e.g., prediction intervals, probability of exceedance maps) and embedding this uncertainty directly into decision-support frameworks for risk-based management [110].

9.4. Assimilation of Novel Data Sources

Research should explore the formal assimilation of non-traditional data sources. This includes using high-resolution remote sensing (e.g., hyperspectral imagery) for surface water quality and investigating methods to incorporate citizen science data, after rigorous quality control, to dramatically increase spatial data density [126].

9.5. Interoperability and Open-Source Platforms

To ensure wide adoption, especially in resource-limited settings, future efforts should prioritize the development of open-source, user-friendly platforms and standardized workflows that integrate GIS, interpolation tools, and data preprocessing pipelines. This will promote reproducibility and collaborative development [128-130].

9.6. Interdisciplinary and Systems-Based Approaches

Increasingly, the field is transitioning toward holistic, systems-based solutions that integrate environmental chemistry, process engineering, informatics, and data science. This shift is essential to address both the technical and regulatory challenges posed by evolving effluent standards, sustainability imperatives, and the complex nature of wastewater sources [131-140]. Precise, high-resolution characterization supports the development of effective policies, early warning systems, and the design of innovative treatment processes, which reduce environmental and public health risks.

9.7. Frontiers: Membrane and Hybrid Technologies

Innovations in membrane bioreactors, combined physicochemical-biological systems, and advanced oxidation are creating new demands for feed characterization, particularly for constituents that affect fouling, biodegradability, or removal efficiency [137,141]. High-resolution input characterization, driven by advanced analytics and real-time monitoring, will be crucial in maximizing the performance and sustainability of these next-generation treatment train designs. In summary, future wastewater characterization is increasingly focused on real-time, high-resolution, and predictive modalities, enabled by the integration of smart sensor networks, multivariate statistical and machine learning analytics, and interdisciplinary systems thinking. This convergence is crucial for enabling adaptive, efficient, and sustainable wastewater management that meets 21st-century environmental and public health requirements [133,139].

10. Conclusions

This review has synthesized the transformative role of GIS and statistical interpolation in understanding and managing wastewater characteristics. We have critically evaluated the methodological spectrum, arguing that the choice of technique is not merely technical but strategic, contingent on data structure, the phenomenon's spatial behavior, and the decision context. Our meta-analysis provides quantitative support for the shift towards advanced methods, demonstrating that machine learning and hybrid models can significantly enhance prediction accuracy. While traditional methods like IDW and Kriging remain essential tools, particularly in data-sparse contexts, the field's advancement is now quantitatively linked to the integration of ML. The development of hybrid models that leverage the respective strengths of these paradigms is the most promising path forward for complex, nonlinear systems.

The paramount challenge remains translating spatial predictions into confident action. This necessitates robust data preprocessing, careful method selection, and most importantly the effective communication of predictive uncertainty. The future of wastewater mapping lies in the transition from static, historical analysis to dynamic, intelligent systems. The integration of real-time sensor networks, AI-driven analytics, and digital twin concepts promises a new era of adaptive management, where spatial interpolation serves as the core of predictive early-warning systems and optimized infrastructure planning. By providing a critical synthesis and a clear research roadmap, this review underscores that the ongoing evolution in spatial interpolation is pivotal for building resilient, sustainable, and intelligent wastewater management systems for the 21st century.

Complete Data for Forest Plot: Figure (2)

Study	Year	RoM	CI_Lower	CI_Upper	Weight
Sun et al.	2009	0.92	0.84	1.01	3.8%
Murphy & Curriero	2010	1.08	0.95	1.23	3.5%
Karandish & Shahnazari	2014	0.95	0.82	1.10	3.2%
Li & Heap	2014	0.89	0.81	0.98	4.1%
Stachelek & Madden	2015	1.02	0.88	1.18	3.1%
Abbas et al.	2019	1.15	0.97	1.36	2.8%
Lu et al.	2020	0.72	0.65	0.80	4.3%
De Jesus et al.	2021	0.88	0.76	1.02	3.4%
Igaz et al.	2021	0.94	0.83	1.06	3.6%
Farzaneh et al.	2022	0.91	0.80	1.04	3.5%
Wagner & Henzen	2022	0.83	0.75	0.92	4.0%
Boumpoulis et al.	2023	0.96	0.85	1.08	3.7%
Zhao	2023	0.75	0.67	0.84	4.2%
Ghosh et al.	2023	0.78	0.69	0.88	4.0%
Biernacik et al.	2023	0.87	0.79	0.96	4.1%
Takoutsing & Heuvelink	2022	0.85	0.77	0.94	4.1%
Tadić et al.	2024	0.81	0.73	0.90	4.1%
Nishimoto et al.	2024	0.93	0.82	1.05	3.6%
Salehi et al.	2024	0.98	0.87	1.10	3.6%
Zaresefat et al.	2024	0.79	0.72	0.87	4.2%
Ayalew & Tegenu	2024	0.90	0.79	1.03	3.5%
Shawky	2025	0.79	0.70	0.89	3.9%
Das	2025	0.68	0.58	0.79	3.7%
Shukla et al.	2025	0.71	0.63	0.80	4.1%
Wang et al.	2025	0.69	0.61	0.78	4.2%
Overall Effect	-	0.816	0.757	0.879	100%